Hi Joe,
I have been thinking more about the Linrad polarization
questions that I raised here two weeks ago.
I wrote:
Suppose they [the feedline lengths in X and Y channels]
are not well matched. In other words, suppose that
the complex gains and signal delays in the two polarization
channels are not equal. Will Linrad's polarization-matching
capability be compromised? As far as I can see, it still works
well even with poorly matched feedlines. I suppose this must
mean that Linrad solves for a differential complex gain, and
that over a fairly narrow bandwidth a different delay can be
treated as a phase shift.
You replied:
From a practical point of view the cables are well matched. I think
it is a safe assumption to guess that the length differences will
be very small and of no concern.
Let's work in terms of the Stokes Parameters, with complex
signals X and Y.
I = |X|^2 + |Y|^2 (total power)
Q = |X|^2 - |Y|^2 (horizontal linear component)
U = 2Re(X^* Y) (vertical linear component)
V = 2Im(X^* Y) (circular component)
L = sqrt(Q^2 + U^2) (linear polarized component)
Theta = 0.5*atan(U/Q) (polarization angle)
If I shift the phase of X relative to Y (say, by inserting
an extra piece of cable in the X feedline), the values of U,
V, L, and Theta will surely change.Yes, of course, but any
difference in length of the cables will be insignificant as
compared to the differences in phase shifts that you have in
the amplifiers.
I don't know what you meant when writing "From a practical
point of view the cables are well matched." In my station,
at present, it would be a complete accident if the downlines
from the tower-mounted X and Y preamps were the same
electrical length. They are just two pieces of coax that I
had lying around.
But I am sure that none of them is VERY long in terms of
wavelengths. It means that the phase shift vs frequency
the difference in cable lenghts introduce is very small and
negligible as compared to the large difference in phase vs
frequency that non-matched RF amplifiers might introduce.
Over a narrow bandwidth, such as 2 MHz, even that can be neglected
if the RF amplifiers are reasonably similar. In the end, you
just have an unknown, but frequency independent phase shift between
the two RF channels.
Moreover, my xpol yagis have the H elements located forward
of the V elements by some 10 inches or so (I forget the
exact amount) -- maybe 1/8 of a wavelength. This will have
a very significant effect, as well, no?
It just adds to the undeterminated phase difference and it
is independent of frequency over 2 MHz.
So, it seems to me that the only way to get things
calibrated correctly is the one you outlined:
Listen to a linearly polarised signal that arrives with similar
strength in both polarisations. (This is the strongest reason
why the X configuration is so much better than the + configuration.
It is easy to find a pure H-pol signal. Finding a 45 degree
terrestrial signal is virtually impossible due to ground reflections
so a + configured system has to be calibrated on EME signals.)
Change cable lengths until the signal appears close to linear
on the pol meter. Fine tune by tweaking the second RF amplifiers.
(will affect both amplitude and phase, but there are two second
RF amplifiers so it should be possible to find both amplitude and
phase matching.
On the other hand, a strong practical reason to use the +
configuration is that one wants to use the antenna for tropo
as well as EME -- and therefore wants the ability to
transmit a horizontal signal. My array, therefore, is in
the + configuration.
But that is a non-argument. I was using the X configuration for
10 years with only the option to put 50% of the power into each
polarisation. In phase for vertical and out of phase for horizontal.
(I also had +/- 90 degrees for circular, but although very good
for aurora I found it useless for EME) I actually lost some interesting
contacts because I could not put all the power in +45 or -45 degrees.
I did hear GW0KZG/MM from the red sea and got QRZ from him.
I knew 45 degrees would have given 3 dB more signal, but I could not
do it because my X configuration was set up in the simple way with
only H or V (or circular) as the emitted polarisation.
It would of course be easy to add parameters for amplitude
and phase balance, but I have not done it since I found
it easy to do in hardware:-)
To me it seems much easier to do it in software, and perhaps
I will try this within MAP65.
OK, but remember there is a performance penalty....
Suppose the gains in the X
and Y channels are already matched. Then, while receiving a
100% horizontally polarized signal, shouldn't it be
sufficient to multiply the complex signal for X (or Y) by a
complex constant e^(i*phi), with the phase shift "phi"
chosen so as to minimize Stokes Parameter V ?
Hmmm, If you have the + configuration, all the energy will
come in one RF channel and there is no phase information.
You will have to listen to an EME signal that you know is linear
and that you find strong enough in both channels to determine
the phase between the signals. Then, when knowing the phase error,
you can shift the phase of fft1_filtercorr[] in Linrad to rotate
the phase angle as desired. Actually I think this would be a good
strategy. The gain should be set in hardware for the compromise
between dynamic range and system noise figure that you want.
Then the phase could be adjusted in software because there is not
really any reason to have it set by hardware. (Although as an
experimenter with many different dual channel receivers I
personally prefer to have matched hardware...)
73
Leif
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